A086121 Positive sums or differences of two cubes of primes.

16, 19, 35, 54, 98, 117, 133, 152, 218, 250, 316, 335, 351, 370, 468, 686, 866, 988, 1206, 1304, 1323, 1339, 1358, 1456, 1674, 1854, 1946, 2072, 2170, 2189, 2205, 2224, 2322, 2540, 2662, 2716, 3528, 3582, 4394, 4570, 4662, 4788, 4886, 4905, 4921, 4940, 5038

Offset

1,1

Links

Hans Havermann and T. D. Noe, Table of n, a(n) for n = 1..20000.

Example

117 and 133 each belong to the (set) sequence because can be written as 117 = 5^3 - 2^3 and 133 = 5^3 + 2^3.

Mathematica

nn=10^6; td=Reap[Do[n=Prime[i]^3-Prime[j]^3; If[n<=nn, Sow[n]], {i, PrimePi[Sqrt[nn/6]]}, {j, i-1}]][[2, 1]]; ts=Reap[Do[n=Prime[i]^3+Prime[j]^3; If[n<=nn, Sow[n]], {i, PrimePi[nn^(1/3)]}, {j, i}]][[2, 1]]; Union[td, ts] (* T. D. Noe, Oct 04 2010 *)
n = 100; Select[Sort@Flatten@ Table[Prime[i]^3 + (-1)^k Prime[j]^3, {i, n}, {j, i}, {k, 2}], 0 < # < (Prime[n] + 2)^3 - Prime[n]^3 &] (* Ray Chandler, Oct 05 2010 *)

Crossrefs

Cf. A086119, A086120. Also see A045636, A045699.

Sequence in context: A249612 A260560 A034012 * A030402 A303813 A335210

Adjacent sequences: A086118 A086119 A086120 * A086122 A086123 A086124

Keyword

nonn

Author

Hollie L. Buchanan II, Jul 11 2003

Extensions

Edited by N. J. A. Sloane, Oct 05 2010 to remove a discrepancy between the terms of the sequence and the b-file. The old Mma program and b-file were wrong.

Status

approved